Above, h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and is the viscous dissipation function.

High temperatures discussed previously as a manifestation of viscous dissipation cause non-equilibrium chemical flow properties such as vibrational excitation, dissociation and ionization of molecules resulting in convective and radiative heat-flux.

Some authors dispute that Mars ' obliquity is chaotic, and show that tidal dissipation and viscous core-mantle coupling are adequate for it to have reached a fully damped state, similar to Mercury and Venus.

Many other phenomena, such as the relative motion of bodies with friction, or viscous motion of fluids, reduce to this, because the underlying mechanism is the dissipation of usable energy ( for example, kinetic energy ) into heat.

In this range, the energy input from nonlinear interactions and the energy drain from viscous dissipation are in exact balance.

Eventually this process creates structures that are small enough that molecular diffusion becomes important and viscous dissipation of energy finally takes place.

If the process is performed more slowly, the frictional or viscous dissipation is less.

The heating of the disk is primarily caused by the viscous dissipation of turbulence in it and by the infall of the gas from the nebula.

Movement of tides causes a loss of mechanical energy in the Earth – Moon system: this is a result of pumping of water through natural restrictions around coastlines and consequent viscous dissipation at the seabed and in turbulence.

In the superfluid component, however, vorticity is restricted to the quantized vortex lines, and there is no viscous dissipation.

This leads to the generation of vorticity and viscous dissipation of kinetic energy in the boundary layer.

In the limit of small angle ( i. e., immediately before the coin stops spinning ), air drag ( specifically, viscous dissipation ) is the dominant factor, but prior to this rolling friction is the dominant effect.

Recent research was sparked by an article in the April 20, 2000 edition of Nature, where Keith Moffatt shows that viscous dissipation in the thin layer of air between the disk and the table is sufficient to account for the observed abruptness of the settling process.

Moffatt shows that, as time approaches a particular time ( which is mathematically a constant of integration ), the viscous dissipation approaches infinity.

Moffatt responded with a generalized theory that should allow experimental determination of which dissipation mechanism is dominant, and pointed out that the dominant dissipation mechanism would always be viscous dissipation in the limit of small ( angle between the coin and the surface, i. e., just before the coin settles ).

where is the dissipation of kinetic energy of the filtered velocity field by viscous stress, and represents the sub-filter scale ( SFS ) dissipation of kinetic energy.

In addition, if all human hemoglobin were free in the plasma rather than being contained in RBCs, the circulatory fluid would be too viscous for the cardiovascular system to function effectively.

The magnitude of Trq < sub > d </ sub > comes from the slip limiting mechanism in the differential and may be a function of input torque as in the case of a gear differential or the difference in the output speeds as in the case of a viscous differential.

* shock absorption-as a dilatant fluid, synovial fluid is characterized by the rare quality of becoming more viscous under applied pressure ; the synovial fluid in diarthrotic joints becomes thick the moment shear is applied in order to protect the joint and subsequently thins to normal viscosity instantaneously to resume its lubricating function between shocks

As cooling progresses, honey will become more viscous at an increasingly rapid rate, reaching 600 poise around.

The classical theory of fluid mechanics, governed by the Navier-Stokes equation, deals with the behaviour of viscous fluids, for which, according to Newton's Law, the stress is directly proportional to the rate of strain, but independent of the strain itself.

** if the material deformation rate increases linearly with increasing applied stress, then the material is viscous in the Newtonian sense.

The reduction in absorption rate with guar gum may be due to the increased resistance by viscous solutions to the convective flows created by intestinal contractions.

As flow rate increases, greater viscous and pressure forces on the float cause it to rise until it becomes stationary at a location in the tube that is wide enough for the forces to balance.

The classical theory of hydrodynamics describes the properties of viscous fluid, for which the response of stress is dependent on strain rate.

If a Maxwell material is suddenly subjected to a stress, then the elastic element would suddenly deform and the viscous element would deform with a constant rate:

However, dissolving the cellulose at a fast enough rate to make it commercially profitable requires the cellulose dope to be in a highly viscous and concentrated state.

After this elastic phase, uplift proceeded by slow viscous flow so the rate of uplift decreased exponentially after that.

The magnitude of the viscous stresses depends upon the rate of deformation.

The viscous components can be modeled as dashpots such that the stress-strain rate relationship can be given as,

Since the mantle is extremely viscous, the mantle flow rate varies in pulses which are reflected in the lithosphere by small amplitude, long wavelength undulations.

Several vapour-vesicles may unite while the rock is still viscous, and thus form a large cavity which may become the home of an agate of exceptional size ; thus a Brazilian geode lined with amethyst and weighing 35 tons was exhibited at the Düsseldorf Exhibition of 1902.

The internal chamber is filled with a viscous ink that is dispensed at its tip during use by the rolling action of a small sphere.

Glasses containing both boron and phosphorus ( borophosphosilicate glass, BPSG ) undergo viscous flow at lower temperatures ; around 850 ° C is achievable with glasses containing around 5 weight % of both constituents, but stability in air can be difficult to achieve.

Stokes flow is flow at very low Reynolds numbers, Re << 1, such that inertial forces can be neglected compared to viscous forces.

Glasses are amorphous solids ( e. g. amorphous materials that are at temperatures below the glass transition temperature ) which are usually fabricated when the viscous molten material cools very rapidly to below its glass transition temperature, without sufficient time for a regular crystal lattice to form.

A parameter of particular interest in synthetic polymer manufacturing is the glass transition temperature ( T < sub > g </ sub >), which describes the temperature at which amorphous polymers undergo a transition from a rubbery, viscous amorphous liquid, to a brittle, glassy amorphous solid.

This uniformity can be explained by detailed fluid-mechanical modelling, which shows that the resist moves much faster at the top of the layer than at the bottom, where viscous forces bind the resist to the wafer surface.

When such bodies are subjected to a sinusoidally oscillating stress, the strain is neither exactly in phase with the stress ( as it would be for a perfectly elastic solid ) nor 90 degrees out of phase ( as it would be for a perfectly viscous liquid ) but rather exhibits a strain that lags the stress at a value between zero and 90 degrees: i. e., Some of the energy is stored and recovered in each cycle, and some is dissipated as heat.

* By contrast, elastic and viscous ( or intermediate, viscoelastic ) behaviour is relevant at short times ( transient behaviour ):</ br > We again consider the application of a constant stress:

granite can flow plastically with a vanishingly small yield stress at room temperatures, ( i. e. a viscous flow ).

Under low Reynolds numbers viscous effects dominate and the flow is laminar, whereas at high Reynolds numbers inertia predominates and the flow may be turbulent.

This magma tends to be very viscous due to its high silica content, so often does not reach the surface and cools at depth.

Earthflows are downslope, viscous flows of saturated, fine-grained materials, which move at any speed from slow to fast.

Heat treatment of a xerogel at elevated temperature produces viscous sintering ( shrinkage of the xerogel due to a small amount of viscous flow ) and effectively transforms the porous gel into a dense glass.

A portion of the large kinetic energy associated with flow at high Mach numbers transforms into internal energy in the fluid due to viscous effects.

These are similar to air displacement pipettes, but are less commonly used and are used to avoid contamination and for volatile or viscous substances at small volumes, such as DNA.

Since eddies in this range are much larger than the dissipative eddies that exist at Kolmogorov scales, kinetic energy is essentially not dissipated in this range, and it is merely transferred to smaller scales until viscous effects become important as the order of the Kolmogorov scale is approached.

Thus, in cases of very viscous flows ( e. g. Couette Flow ), the vorticity will be diffused throughout the flow field and it is probably simpler to look at the velocity field ( i. e. vectors of fluid motion ) rather than look at the vorticity field ( i. e. vectors of curl of fluid motion ) which is less intuitive.

The thickness of the velocity boundary layer is normally defined as the distance from the solid body at which the viscous flow velocity is 99 % of the freestream velocity ( the surface velocity of an inviscid flow ).